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ABSTRACT Rapid formation of supermassive black holes occurs in dense nuclear star clusters that are initially gas-dominated. Stellar-mass black hole remnants of the most massive cluster stars sink into the core, where a massive runaway black hole forms as a consequence of combined effects of repeated mergers and Eddington-limited gas accretion. The associated gravitational wave signals of high-redshift extreme mass-ratio inspirals are a unique signature of the nuclear star cluster scenario. 

ABSTRACT We present predictions for the high-redshift halo–galaxy–supermassive black hole (SMBH) connection from the Trinity model. Matching a comprehensive compilation of galaxy (0 ≤ z ≤ 13) and SMBH data sets (0 ≤ z ≤ 6.5), Trinity finds: (1) The number of SMBHs with M• > 109 M⊙ in the observable Universe increases by five orders of magnitude from z ∼ 10 to z ∼ 2, and by another factor of ∼3 from z ∼ 2 to z = 0; (2) The M• > 109 and 1010 M⊙ SMBHs at z ∼ 6 live in haloes with ∼(2 − 3) and (3 − 5) × 1012 M⊙; (3) the newly discovered JWST AGN candidates at 7 ≲ z ≲ 11 are overmassive compared to the intrinsic SMBH mass–galaxy mass relation from Trinity, but they are still broadly consistent with Trinity predictions for flux limited AGN samples with Lauer bias. This bias favours the detection for overmassive SMBHs due to higher luminosities at a fixed Eddington ratio. However UHZ1’s M•/M* ratio is still some 1 dex higher than Trinity AGNs, indicating a discrepancy; (4) Trinity underpredicts the number densities of GN-z11 and CEERS_1019 analogues. But given the strong constraints from existing data in Trinity, the extra constraint from GN-z11 and CEERS_1019 does not significantly change trinity model results. (5) z = 6–10 quasar luminosity functions will reduce uncertainties in the trinity prediction of the z = 6–10 SMBH mass–galaxy mass relation by up to ∼0.5 dex. These luminosity functions will be available with future telescopes, such as Roman and Euclid. 

ABSTRACT Large-scale magnetic fields in the nuclear regions of protogalaxies can promote the formation and early growth of supermassive black holes (SMBHs) by direct collapse and magnetically boosted accretion. Turbulence associated with gravitational infall and star formation can drive the rms field strength toward equipartition with the mean gas kinetic energy; this field has a generic tendency to self-organize into large coherent structures. If the poloidal component of the field (relative to the rotational axis of a star-forming disc) becomes organized on scales ≲r and attains an energy of order a few per cent of the turbulent energy in the disc, then dynamo effects are expected to generate magnetic torques capable of increasing the inflow speed and thickening the disc. The accretion flow can transport matter towards the centre of mass at a rate adequate to create and grow a massive direct-collapse black hole seed and fuel the subsequent AGN at a high rate, without becoming gravitationally unstable. Fragmentation and star formation are thus suppressed and do not necessarily deplete the mass supply for the accretion flow, in contrast to prevailing models for growing and fuelling SMBHs through disc accretion. 

ABSTRACT Using recent empirical constraints on the dark matter halo–galaxy–supermassive black hole (SMBH) connection from z = 0–7, we infer how undermassive, typical, and overmassive SMBHs contribute to the quasar luminosity function (QLF) at z = 6. We find that beyond Lbol = 5 × 1046 erg s−1, the z = 6 QLF is dominated by SMBHs that are at least 0.3 dex above the z = 6 median M•–M* relation. The QLF is dominated by typical SMBHs (i.e. within ±0.3 dex around the M•–M* relation) at Lbol ≲ 1045 erg s−1. At z ∼ 6, the intrinsic M•–M* relation for all SMBHs is slightly steeper than the z = 0 scaling, with a similar normalization at $$M_* \sim 10^{11} \, \mathrm{M}_\odot$$. We also predict the M•–M* relation for z = 6 bright quasars selected by different bolometric luminosity thresholds, finding very good agreement with observations. For quasars with Lbol > 3 × 1046 (1048) erg s−1, the scaling relation is shifted upwards by ∼0.35 (1.0) dex for 1011M⊙ galaxies. To accurately measure the intrinsic M•–M* relation, it is essential to include fainter quasars with Lbol ≲ 1045 erg s−1. At high redshifts, low-luminosity quasars are thus the best targets for understanding typical formation paths for SMBHs in galaxies. 

ABSTRACT We present Trinity, a flexible empirical model that self-consistently infers the statistical connection between dark matter haloes, galaxies, and supermassive black holes (SMBHs). Trinity is constrained by galaxy observables from 0 < z < 10 [galaxies’ stellar mass functions, specific and cosmic star formation rates (SFRs), quenched fractions, and UV luminosity functions] and SMBH observables from 0 < z < 6.5 (quasar luminosity functions, quasar probability distribution functions, active black hole mass functions, local SMBH mass–bulge mass relations, and the observed SMBH mass distributions of high-redshift bright quasars). The model includes full treatment of observational systematics [e.g. active galactic nucleus (AGN) obscuration and errors in stellar masses]. From these data, Trinity infers the average SMBH mass, SMBH accretion rate, merger rate, and Eddington ratio distribution as functions of halo mass, galaxy stellar mass, and redshift. Key findings include: (1) the normalization and the slope of the SMBH mass–bulge mass relation increases mildly from z = 0 to z = 10; (2) The best-fitting AGN radiative+kinetic efficiency is ∼0.05–0.06, but can be in the range ∼0.035–0.07 with alternative input assumptions; (3) AGNs show downsizing, i.e. the Eddington ratios of more massive SMBHs start to decrease earlier than those of lower mass objects; (4) The average ratio between average SMBH accretion rate and SFR is ∼10−3 for low-mass galaxies, which are primarily star-forming. This ratio increases to ∼10−1 for the most massive haloes below z ∼ 1, where star formation is quenched but SMBHs continue to accrete. 

Abstract Current theoretical models predict a mass gap with a dearth of stellar black holes (BHs) between roughly 50 M ⊙ and 100 M ⊙ , while above the range accessible through massive star evolution, intermediate-mass BHs (IMBHs) still remain elusive. Repeated mergers of binary BHs, detectable via gravitational-wave emission with the current LIGO/Virgo/Kagra interferometers and future detectors such as LISA or the Einstein Telescope, can form both mass-gap BHs and IMBHs. Here we explore the possibility that mass-gap BHs and IMBHs are born as a result of successive BH mergers in dense star clusters. In particular, nuclear star clusters at the centers of galaxies have deep enough potential wells to retain most of the BH merger products after they receive significant recoil kicks due to anisotropic emission of gravitational radiation. Using for the first time simulations that include full stellar evolution, we show that a massive stellar BH seed can easily grow to ∼10 3 –10 4 M ⊙ as a result of repeated mergers with other smaller BHs. We find that lowering the cluster metallicity leads to larger final BH masses. We also show that the growing BH spin tends to decrease in magnitude with the number of mergers so that a negative correlation exists between the final mass and spin of the resulting IMBHs. Assumptions about the birth spins of stellar BHs affect our results significantly, with low birth spins leading to the production of a larger population of massive BHs.